Aggregate demand uncertainty outbreaks and employment hysteresis in G7 countries

AbstractThe slow recovery following the recent financial crisis in many developed countries, and the predictable long lasting economic effects of the Covid-19 pandemic have raised a new interest on the topic of employment hysteresis. In the presence of hysteresis there is no predetermined long-run equilibrium level of aggregate employment. As the economic system is not self-adjusting toward a unique equilibrium, timely, and sustained expansionary macroeconomic policies should be applied to mitigate the impact of negative shocks. The purpose of this paper is to uncover hysteresis effects in the macrodynamics of employment along with variations in its intensity that may result from outbreaks in aggregate demand uncertainty. We estimate a switching employment equation based on the play model of hysteresis, which describes a dynamic process whereby non-convex adjustment costs and uncertainty create intervals of weak reaction of employment to small changes in forcing variables, but spurts in the reaction to large demand shocks. As a novel feature, the estimation allows the presence of structural breaks in the value of the switching parameter of the employment equation due to aggregate demand uncertainty outbreaks. We have concluded that hysteresis effects increased in general in crisis periods associated to outbreaks of uncertainty in aggregate demand.Keywords: Employmenthysteresisuncertaintystructural breaksJEL CLASSIFICATION CODES: E24J23 Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Local input extrema that are not followed by an absolute extrema (see, e.g., Cross et al. Citation2005).2 Therefore, hysteresis should not be confused with the presence of a unit root in a linear dynamic system, or zero root in continuous time difference equations (see Amable et al. Citation1993, Citation1994). The consequence is that non-stationary econometrics cannot be used to overcome the role of uncertainty and to make predictions about the future on the basis of past data. This issue has been put forward by Davidson (Citation1993) concerning the adequacy of the concept of hysteresis in the context of post Keynesian economics.3 For example, uncertainty about the course of technical progress, the future behavior of prices, the outcome of plan of investment, not to mention the effects of natural and political cataclysms with economic impact (Robinson Citation1974, 1).4 The possibility that the firms have to adjust labor input along the intensive margin, i.e., fluctuations in hours worked per employee, may also enhance the employment hysteresis effects (Mota, Varejão, and Vasconcelos Citation2012).5 The importance of the initial conditions and path dependence as drivers of the outcome of economic system was early recognized by Robinson (Citation1974).6 See also Rios, Rachinskii, and Cross (Citation2017).7 This is perfectly compatible with the concept of hysteresis. In fact “…hysteresis involves explicit structural change in the system that is determining long-run outcomes. Hence a hysteretic system may actively create its own set of final outcomes in the course of its evolution as a result of this structural change. With hysteresis, then, whilst definitive final outcomes – such as equilibria – are possible, it may only be within our powers to identify these outcomes ex post, after they have actually been established. They need not exist ex ante, independently of the actual history of adjustments in the system to which they pertain.” Setterfield (Citation1998, 294)8 See Benigno and Fornaro (Citation2018); Cerra, Saxena, and Panizza (Citation2013); Garga and Singh (Citation2021), Jordà, Singh, and Taylor (Citation2020); Reifschneider, Wascher, and Wilcox (Citation2015), for recent evidence of permanent effects of monetary policy.9 As the wedge between private and public returns on investments in R&D increases typically during recessions, the State should subsidize particularly the investment in innovation (see Bianchi et al. Citation2019). Besides, monetary policy should be adequately expansionary to reduce the liquidity risk of long-term investments in innovation (see Aghion et al. Citation2012).10 A concept that was not familiar to Keynes.11 Keynes was part of a long tradition rejecting the view that the economic system is self-adjusting to a general equilibrium (see Kregel Citation2011, 271, for a survey of the literature).12 The switching parameter of the employment equation is interpreted as an ‘aggregate employment band on inaction,’ which summarizes the magnitude of the hysteretic effects (Mota, Varejão, and Vasconcelos Citation2015).13 Although originally applied in the physics of magnetics, the Preisach model should be viewed as a new mathematical idea that can be applied to describe a wide range of hysteretic phenomena in quite different areas, including aggregate employment dynamics (see, e.g., Amable et al. Citation1993, Citation1994; Cross Citation1994, Citation1997; Cross et al. Citation2005; Mayergoyz Citation2021.14 We assume that the exogenous component of aggregate demand, xt, determines the state of firm’s activity through its impact in the price level, which corresponds to the gross revenue under the assumptions of the model.15 Firm also incur in sunk costs for the acquisition of physical assets like firm specific equipment or intangible assets such as reputation, acquired by investments in marketing and advertising, or technical knowledge (see, e.g., Belke, Baudisch, and Göcke Citation2020; Dias and Shackleton Citation2011; Folta, Johnson, and O’Brien Citation2006; Pindyck Citation1988, Citation1991). Other non-firm specific investments like office equipment, cars, trucks and computers can have a resale value well below their purchase cost due to the ‘lemons’ problem (Pindyck Citation1991, 1111). Furthermore, to enter new markets, firms often have to incur irreversible costs, e.g., for gathering information on market revenues, creating distribution and servicing networks, and advertising or establishing a brand name (see, Adamonis and Göcke Citation2019).16 EquationEquation (1)(1) Rαj,βj(xt)={1, if Rαj,βj(xt−1)=0 and xt≥βj [entry in the market] orRαj,βj(xt−1)=1 and xt>αj [stay active in the market]0, if Rαj,βj(xt−1)=0 and xt<βj [stay inactive] or Rαj,βj(xt−1)=1 and xt≤αj [exit the market](1) is derived from a profit maximizing problem in discrete time with an infinite plan horizon, and a discount factor, δ=11+i, where i is the interest rate (see, e.g., Göcke Citation2002, 118, and Mota et al. Citation2012 for a complete description of the model).17 Within the assumptions of the model the trigger values for exit and entry are αj=wj−δFj and βj=wj+δHj respectively (see, e.g., Göcke Citation2002; Mota, Varejão, and Vasconcelos Citation2012).18 This stylized model can offer a good description of the employment dynamics if we consider a firm disaggregated into single production units, each of them represented by a non-ideal relay operator (see Belke and Göcke Citation1999; Cross Citation2014). Therefore, in this setting the decision to enter the market is similar to the hiring decision, and the decision to exit the market is analogous to the firing decision.19 This matches with the empirical observation of discontinuous and irregular adjustment of employment by firms, in which periods of inaction are punctuated by episodes of large adjustment (see e.g., Caballero, Engel, and Haltiwanger Citation1997; Hamermesh Citation1989; Mota, Varejão, and Vasconcelos Citation2012; Varejão and Portugal Citation2007).20 The heterogeneity in the way firms react to aggregate demand shocks arises from specific cost structures including non-convex adjustment costs (that may depend on firms’ age, size, ownership, average work skill level and innovation), and from the way firms deal with uncertainty (see, Gaëlle and Scarpetta Citation2006).21 See Cross et al. (Citation2005); Piscitelli et al. (Citation2000), for a more comprehensive description of the geometric description of the Preisach model of hysteresis.22 As we assume that firms are uniformly distributed in the Preisach triangle, the branches of the hysteresis loop are quadratic functions.23 At the firm level there are only two branches, and the transition between those branches only occurs when xt increases above βj or decreases below αj.24 This follows from the wiping-out property of the Preisach model (see, Mayergoyz Citation2003).25 For a complete description of the Preisach model of hysteresis see, e.g. Mayergoyz (Citation2003); Mota and Vasconcelos (Citation2012).26 See Cross et al. (Citation2010); Göcke and Werner (Citation2015); Piscitelli et al. (Citation1999) for theoretical models with feedback effects of the system on the equilibrium level of the hysteretic forcing variable.27 See also Amable et al (Citation1993, Citation1994).28 The linear play model of hysteresis (the term is used because of its analogy to play in mechanics) can be viewed as a piecewise-linear approximation of the Preisach hysteresis loop, where the slope of the linear functions change at extrema (see, Krasnosel’skii and Pokrovskii Citation1989; Visitin Citation1994).29 A general description of the model can be found in Visitin (Citation1994).30 This can be the result of an exogenous shock or endogenously caused by the decrease of demand. In fact, of a lack of aggregate demand and increasing unemployment can be viewed as the result of the malfunctioning of the economy and thus affects business confidence.31 The sequence xt1→xt2→xt3 originates as counter-clockwise oriented loop abcde.32 Although real wages could also be a source of hysteresis, our aim is to test the presence of hysteresis caused by aggregate demand shocks. Therefore, real wages enters as a non-hysteretic explanatory variable in the employment equation. For the joint influence of several inputs in an economic system with hysteresis see Göcke (Citation2019).33 We assume that the demand for employment results from consumers’ demand for final goods and services (that determines a scale effect), and the availability of employment that determines its price (input substitution effect). Therefore, we include in the employment equation the traditional explanatory variables (we follow Hamermesh, Citation1993, 30 and 64).34 See also Belke and Göcke (Citation2001a, Citation2001b); Göcke (Citation2001) for more detail.35 See Mota and Vasconcelos (Citation2021) for a detailed description of this new version of the play algorithm.36 Equation (4) is based on a piecewise linear relationship between Nt and xt where the play lines and the spurt lines are connected continuously by knots. In Figure 3 the knots are points a, b, c, d, e, and f when the input follows the sequence xt0→ xt1→xt2→xt3. The position of the knots are a priori unknown, because they depend on the width of the play interval, γ, which has to be estimated, and on the position of the play line that is determined by the past values of xt. Since the adjacent play and spurts lines are connected, the employment equation is a special case of a switching regression with an unknown splitting factor that in the context of the play model corresponds to the width γt (see Figure 3), and similar to a linear spline function (see Poirier Citation1973, Citation1976). In this case, the OLS estimator is asymptotically consistent and normal distributed under the standard regression model assumptions (see Hinkley Citation1969; Hudson Citation1966; Poirier Citation1976).37 Note that is this model there is a combination of structural changes of a non-temporal nature in the relationship between aggregate employment, Nt, and aggregate demand captured by xt that arises from reversals of xt, and from subsequently cumulated variations surpassing the play interval, and structural changes in the time domain due to changes in the play interval itself due to demand uncertainty outbreaks.38 For the variables in levels the augmented Dickey-Fuller test statistic (with an intercept included in the test equation) is in general larger than the 1% critical value (−3.509), indicating that we do not reject the non-stationary of the series (Appendix 2). For the first difference of the series, we reject in general the hypothesis of the existence of a unit root (test statistic is smaller than the 1% critical value). We conclude that in general the variables are integrated of order one, I(1). The exceptions is xt that is stationary in levels for France, Germany and for the UK. Nt that is also stationary in levels for the UK. Nt for France and Wt for the United States are I(3).39 The Johansen Test Procedure was used for cointegration testing. Based on the trace test performed with four lags in the VAR representation, and with an intercept in the cointegrating employment EquationEquation (3)(3) Nt=β0+β1xt+β2St(γt)+β3Wt+εt(3) , have concluded that the variables in Equation (3) are cointegrated of rank one in the cases of Canada, Germany, and Italy; cointegrated of rank two in the cases of France, Japan, and USA; and cointegrated of rank four for the UK (the trace test statistic and the critical value for a 5% significance level for the rejection of the hypothesis of no cointegration is reported in Table 2).40 FM-OLS estimator modifies least squares with semiparametric corrections that account for serial correlation effects and for endogeneity in the regressors that result from the existence of cointegrating relationships (Phillips Citation1995; Phillips and Hansen Citation1990).41 For 1% significance level.42 The properties of the inference mentioned before are based on large sample theory and might not be accurate approximations in small size samples (See Hinkley Citation1969 ; Poirier Citation1976). In fact, the distribution of the estimator may converge slowly to normality. Nonetheless, the high value of the Wald test statistic (especially tat concerns the spurt variable) makes us confident of the significance of the estimates.Additional informationFundingThis research has been financed by Portuguese Public Funds through FCT (Portuguese Foundation for Science and Technology) and by the European Regional Development Fund through COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) – in the framework of the project POCI-01-0145-FEDER-006890.Notes on contributorsPaulo R. MotaPaulo R. Mota is at School of Economics and Business and CEF.UP, University of Porto.